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NotesECN741-page9 - ECN 741 Public Economics Fall 2008...

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ECN 741: Public Economics Fall 2008 Differentiate w.r.t α and set α = 1 we get n k =1 U ik c k U i = n k =1 U jk c k U j Also, note that U l = W l , U li = W lg G i and U i = W g G i . Therefore, H i = - n k =1 U ik c k U i - U il l U i = - n k =1 U ik c k U i - W lg l W g = H j This can be generalized to utility functions of the form u ( c 1 , . . . , c k , G ( c k +1 , . . . , c n ) , l ) in which, G ( · ) is homothetic. Then the result is that commodities ( c k +1 , . . . , c n ) should be taxed at uniform rate. Exercise: Suppose consumer is endowed with y unit of good one that cannot be taxed away. Does the uniform commodity taxation still hold? what if the utility function is additive separable? Exercise: Suppose government is restricted to setting taxed on c 1 to zero. How would modify the Ramsey problem? Does the uniform commodity taxation hold?
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